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http://dx.doi.org/10.7468/mathedu.2021.60.1.229

Examining teachers' noticing competency on students' problem-solving strategies: Focusing on errors in fraction addition and subtraction with uncommon denominators problems  

Son, Taekwon (Korea National University of Education)
Hwang, Sunghwan (Seoul Gaju Elementary School)
Publication Information
The Mathematical Education / v.60, no.2, 2021 , pp. 229-247 More about this Journal
Abstract
Students' mathematical thinking is represented via various forms of outcomes, such as written response and verbal expression, and teachers could infer and respond to their mathematical thinking by using them. This study analyzed 39 elementary teachers' competency to notice students' problem-solving strategies containing mathematical errors in fraction addition and subtraction with uncommon denominators problems. Participants were provided three types of students' problem-solving strategies with regard to fraction addition and subtraction problems and asked to identify and interpret students' mathematical understanding and errors represented in their artifacts. Moreover, participants were asked to design additional questions and problems to correct students' mathematical errors. The findings revealed that first, teachers' noticing competency was the highest on identifying, followed by interpreting and responding. Second, responding could be categorized according to the teachers' intentions and the types of problem, and it tended to focus on certain types of responding. For example, in giving questions responding type, checking the hypothesized error took the largest proportion, followed by checking the student's prior knowledge. Moreover, in posing problems responding type, posing problems related to student's prior knowledge with simple computation took the largest proportion. Based on these findings, we suggested implications for the teacher noticing research on students' artifacts.
Keywords
problem-solving strategy; mathematical thinking; error; teacher noticing; fraction addition and subtraction with uncommon denominators; student material;
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